Re: [理工] [工數]-ode
※ 引述《smallprawn (水中瑕)》之銘言：
: 利用降階法解
: 3
: (x -x)u''+(x -3)u'=0
: u=?
: 請高手解摟!!感恩!!
令v = u'
3
(x - x)v' + (x-3)v = 0
3
(x - x)dv + (x-3)vdx = 0
1 x-3
---dv + ---------dx = 0
v 2
x(x - 1)
1 3 -2 -1
---dv + (--- + ----- + -----)dx = 0
v x x+1 x-1
-3 2
v = c1x (x+1) (x-1)
-3 2
u = ∫c1x (x+1) (x-1)dx
3 2
x + x - x - 1
= ∫c1(---------------)dx
x^3
1 1
= c1(x + lnx + --- + ----) + c2
x 2
2x
應該是這樣子吧@@
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